Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 79.6% → 94.0%

Time: 15.7s

Alternatives: 13

Speedup: 0.9×

• 37.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-9 \cdot x, \frac{y}{z}, \mathsf{fma}\left(4 \cdot a, t, \frac{-b}{z}\right)\right)}{-c}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-57}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* -9.0 x) (/ y z) (fma (* 4.0 a) t (/ (- b) z))) (- c))))
   (if (<= z -1.95e-38)
     t_1
     (if (<= z 7e-57)
       (/ (fma (* 9.0 x) y (fma (* (* -4.0 z) a) t b)) (* c z))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((-9.0 * x), (y / z), fma((4.0 * a), t, (-b / z))) / -c;
	double tmp;
	if (z <= -1.95e-38) {
		tmp = t_1;
	} else if (z <= 7e-57) {
		tmp = fma((9.0 * x), y, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(-9.0 * x), Float64(y / z), fma(Float64(4.0 * a), t, Float64(Float64(-b) / z))) / Float64(-c))
	tmp = 0.0
	if (z <= -1.95e-38)
		tmp = t_1;
	elseif (z <= 7e-57)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-9.0 * x), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(N[(4.0 * a), $MachinePrecision] * t + N[((-b) / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision]}, If[LessEqual[z, -1.95e-38], t$95$1, If[LessEqual[z, 7e-57], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e-38 or 6.99999999999999983e-57 < z

   1. Initial program 66.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. div-inv N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      4. flip-+ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}} \cdot \frac{1}{z \cdot c} \]

      5. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}}} \cdot \frac{1}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}} \cdot \frac{1}{\color{blue}{z \cdot c}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}} \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

      8. frac-times N/A

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{z}}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b} \cdot c}} \]

      9. div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{z}}}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b} \cdot c} \]

   4. Applied rewrites 67.6%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{1}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)} \cdot c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + -4 \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{a \cdot t}{c} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

      4. associate--l+ N/A

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x \cdot y}{c \cdot z}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      9. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{\frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\color{blue}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\frac{b}{c \cdot z} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}}\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \frac{b}{c \cdot z} + \color{blue}{-4} \cdot \frac{a \cdot t}{c}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \frac{b}{c \cdot z}\right) \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{c \cdot z}\right)}\right) \]

   7. Applied rewrites 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)} \]

   8. Taylor expanded in c around -inf

      \[\leadsto -1 \cdot \color{blue}{\frac{-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)}{c}} \]
   9. Step-by-step derivation

   10. Applied rewrites 95.1%

       \[\leadsto \frac{\mathsf{fma}\left(-9 \cdot x, \frac{y}{z}, \mathsf{fma}\left(4 \cdot a, t, \frac{-b}{z}\right)\right)}{\color{blue}{-c}} \]

   if -1.95e-38 < z < 6.99999999999999983e-57

   1. Initial program 93.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. associate-+l- N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      4. sub-neg N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{x \cdot 9}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      10. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      11. associate-+l- N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      12. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)} + b\right)}{z \cdot c} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right)\right) + b\right)}{z \cdot c} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right)\right) + b\right)}{z \cdot c} \]

      15. associate-*l* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right)\right) + b\right)}{z \cdot c} \]

      16. distribute-lft-neg-in N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      17. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      18. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      19. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a, t, b\right)}\right)}{z \cdot c} \]

   4. Applied rewrites 90.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot x, \frac{y}{z}, \mathsf{fma}\left(4 \cdot a, t, \frac{-b}{z}\right)\right)}{-c}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-57}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot x, \frac{y}{z}, \mathsf{fma}\left(4 \cdot a, t, \frac{-b}{z}\right)\right)}{-c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{c \cdot z} \cdot \left(9 \cdot x\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-132}:\\ \;\;\;\;\left(\left(\frac{1}{c} \cdot t\right) \cdot a\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-213}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -2e+80)
     (* (/ y (* c z)) (* 9.0 x))
     (if (<= t_1 -1e-132)
       (* (* (* (/ 1.0 c) t) a) -4.0)
       (if (<= t_1 5e-213)
         (/ b (* c z))
         (if (<= t_1 5e-22)
           (* (* (/ a c) t) -4.0)
           (* (* (/ x (* c z)) 9.0) y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -2e+80) {
		tmp = (y / (c * z)) * (9.0 * x);
	} else if (t_1 <= -1e-132) {
		tmp = (((1.0 / c) * t) * a) * -4.0;
	} else if (t_1 <= 5e-213) {
		tmp = b / (c * z);
	} else if (t_1 <= 5e-22) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = ((x / (c * z)) * 9.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    if (t_1 <= (-2d+80)) then
        tmp = (y / (c * z)) * (9.0d0 * x)
    else if (t_1 <= (-1d-132)) then
        tmp = (((1.0d0 / c) * t) * a) * (-4.0d0)
    else if (t_1 <= 5d-213) then
        tmp = b / (c * z)
    else if (t_1 <= 5d-22) then
        tmp = ((a / c) * t) * (-4.0d0)
    else
        tmp = ((x / (c * z)) * 9.0d0) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -2e+80) {
		tmp = (y / (c * z)) * (9.0 * x);
	} else if (t_1 <= -1e-132) {
		tmp = (((1.0 / c) * t) * a) * -4.0;
	} else if (t_1 <= 5e-213) {
		tmp = b / (c * z);
	} else if (t_1 <= 5e-22) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = ((x / (c * z)) * 9.0) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (9.0 * x) * y
	tmp = 0
	if t_1 <= -2e+80:
		tmp = (y / (c * z)) * (9.0 * x)
	elif t_1 <= -1e-132:
		tmp = (((1.0 / c) * t) * a) * -4.0
	elif t_1 <= 5e-213:
		tmp = b / (c * z)
	elif t_1 <= 5e-22:
		tmp = ((a / c) * t) * -4.0
	else:
		tmp = ((x / (c * z)) * 9.0) * y
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -2e+80)
		tmp = Float64(Float64(y / Float64(c * z)) * Float64(9.0 * x));
	elseif (t_1 <= -1e-132)
		tmp = Float64(Float64(Float64(Float64(1.0 / c) * t) * a) * -4.0);
	elseif (t_1 <= 5e-213)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 5e-22)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	else
		tmp = Float64(Float64(Float64(x / Float64(c * z)) * 9.0) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	tmp = 0.0;
	if (t_1 <= -2e+80)
		tmp = (y / (c * z)) * (9.0 * x);
	elseif (t_1 <= -1e-132)
		tmp = (((1.0 / c) * t) * a) * -4.0;
	elseif (t_1 <= 5e-213)
		tmp = b / (c * z);
	elseif (t_1 <= 5e-22)
		tmp = ((a / c) * t) * -4.0;
	else
		tmp = ((x / (c * z)) * 9.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+80], N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * N[(9.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-132], N[(N[(N[(N[(1.0 / c), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 5e-213], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-22], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e80

   1. Initial program 77.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(9 \cdot x\right) \cdot \frac{y}{c \cdot z}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot x\right) \cdot \frac{y}{c \cdot z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 9\right)} \cdot \frac{y}{c \cdot z} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 9\right)} \cdot \frac{y}{c \cdot z} \]

      6. lower-/.f64 N/A

         \[\leadsto \left(x \cdot 9\right) \cdot \color{blue}{\frac{y}{c \cdot z}} \]

      7. *-commutative N/A

         \[\leadsto \left(x \cdot 9\right) \cdot \frac{y}{\color{blue}{z \cdot c}} \]

      8. lower-*.f64 62.6

         \[\leadsto \left(x \cdot 9\right) \cdot \frac{y}{\color{blue}{z \cdot c}} \]

   7. Applied rewrites 62.6%

      \[\leadsto \color{blue}{\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}} \]

   if -2e80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999999e-133

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 78.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 58.0

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 60.3%

      \[\leadsto \left(a \cdot \left(t \cdot \frac{1}{c}\right)\right) \cdot -4 \]

   if -9.9999999999999999e-133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999977e-213

   1. Initial program 85.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 61.9

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 61.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if 4.99999999999999977e-213 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999954e-22

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 68.5

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 68.5%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 71.3%

      \[\leadsto \left(\frac{a}{c} \cdot t\right) \cdot -4 \]

   if 4.99999999999999954e-22 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot x}{c \cdot z} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right)} \cdot y \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right) \cdot y} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right)} \cdot y \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right)} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{x}{c \cdot z}} \cdot 9\right) \cdot y \]

      9. lower-*.f64 62.8

         \[\leadsto \left(\frac{x}{\color{blue}{c \cdot z}} \cdot 9\right) \cdot y \]

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{c \cdot z} \cdot \left(9 \cdot x\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{-132}:\\ \;\;\;\;\left(\left(\frac{1}{c} \cdot t\right) \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-213}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-132}:\\ \;\;\;\;\left(\left(\frac{1}{c} \cdot t\right) \cdot a\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-213}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (* (/ x (* c z)) 9.0) y)))
   (if (<= t_1 -2e+80)
     t_2
     (if (<= t_1 -1e-132)
       (* (* (* (/ 1.0 c) t) a) -4.0)
       (if (<= t_1 5e-213)
         (/ b (* c z))
         (if (<= t_1 5e-22) (* (* (/ a c) t) -4.0) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double t_2 = ((x / (c * z)) * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+80) {
		tmp = t_2;
	} else if (t_1 <= -1e-132) {
		tmp = (((1.0 / c) * t) * a) * -4.0;
	} else if (t_1 <= 5e-213) {
		tmp = b / (c * z);
	} else if (t_1 <= 5e-22) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    t_2 = ((x / (c * z)) * 9.0d0) * y
    if (t_1 <= (-2d+80)) then
        tmp = t_2
    else if (t_1 <= (-1d-132)) then
        tmp = (((1.0d0 / c) * t) * a) * (-4.0d0)
    else if (t_1 <= 5d-213) then
        tmp = b / (c * z)
    else if (t_1 <= 5d-22) then
        tmp = ((a / c) * t) * (-4.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double t_2 = ((x / (c * z)) * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+80) {
		tmp = t_2;
	} else if (t_1 <= -1e-132) {
		tmp = (((1.0 / c) * t) * a) * -4.0;
	} else if (t_1 <= 5e-213) {
		tmp = b / (c * z);
	} else if (t_1 <= 5e-22) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (9.0 * x) * y
	t_2 = ((x / (c * z)) * 9.0) * y
	tmp = 0
	if t_1 <= -2e+80:
		tmp = t_2
	elif t_1 <= -1e-132:
		tmp = (((1.0 / c) * t) * a) * -4.0
	elif t_1 <= 5e-213:
		tmp = b / (c * z)
	elif t_1 <= 5e-22:
		tmp = ((a / c) * t) * -4.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	t_2 = Float64(Float64(Float64(x / Float64(c * z)) * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+80)
		tmp = t_2;
	elseif (t_1 <= -1e-132)
		tmp = Float64(Float64(Float64(Float64(1.0 / c) * t) * a) * -4.0);
	elseif (t_1 <= 5e-213)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 5e-22)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	t_2 = ((x / (c * z)) * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -2e+80)
		tmp = t_2;
	elseif (t_1 <= -1e-132)
		tmp = (((1.0 / c) * t) * a) * -4.0;
	elseif (t_1 <= 5e-213)
		tmp = b / (c * z);
	elseif (t_1 <= 5e-22)
		tmp = ((a / c) * t) * -4.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+80], t$95$2, If[LessEqual[t$95$1, -1e-132], N[(N[(N[(N[(1.0 / c), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 5e-213], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-22], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e80 or 4.99999999999999954e-22 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot x}{c \cdot z} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right)} \cdot y \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right) \cdot y} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right)} \cdot y \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right)} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{x}{c \cdot z}} \cdot 9\right) \cdot y \]

      9. lower-*.f64 62.8

         \[\leadsto \left(\frac{x}{\color{blue}{c \cdot z}} \cdot 9\right) \cdot y \]

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y} \]

   if -2e80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999999e-133

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 78.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 58.0

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 60.3%

      \[\leadsto \left(a \cdot \left(t \cdot \frac{1}{c}\right)\right) \cdot -4 \]

   if -9.9999999999999999e-133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999977e-213

   1. Initial program 85.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 61.9

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 61.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if 4.99999999999999977e-213 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999954e-22

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 68.5

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 68.5%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 71.3%

      \[\leadsto \left(\frac{a}{c} \cdot t\right) \cdot -4 \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{-132}:\\ \;\;\;\;\left(\left(\frac{1}{c} \cdot t\right) \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-213}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-132}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-213}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (* (/ x (* c z)) 9.0) y)))
   (if (<= t_1 -2e+80)
     t_2
     (if (<= t_1 -1e-132)
       (* (* (/ t c) a) -4.0)
       (if (<= t_1 5e-213)
         (/ b (* c z))
         (if (<= t_1 5e-22) (* (* (/ a c) t) -4.0) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double t_2 = ((x / (c * z)) * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+80) {
		tmp = t_2;
	} else if (t_1 <= -1e-132) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t_1 <= 5e-213) {
		tmp = b / (c * z);
	} else if (t_1 <= 5e-22) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    t_2 = ((x / (c * z)) * 9.0d0) * y
    if (t_1 <= (-2d+80)) then
        tmp = t_2
    else if (t_1 <= (-1d-132)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (t_1 <= 5d-213) then
        tmp = b / (c * z)
    else if (t_1 <= 5d-22) then
        tmp = ((a / c) * t) * (-4.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double t_2 = ((x / (c * z)) * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+80) {
		tmp = t_2;
	} else if (t_1 <= -1e-132) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t_1 <= 5e-213) {
		tmp = b / (c * z);
	} else if (t_1 <= 5e-22) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (9.0 * x) * y
	t_2 = ((x / (c * z)) * 9.0) * y
	tmp = 0
	if t_1 <= -2e+80:
		tmp = t_2
	elif t_1 <= -1e-132:
		tmp = ((t / c) * a) * -4.0
	elif t_1 <= 5e-213:
		tmp = b / (c * z)
	elif t_1 <= 5e-22:
		tmp = ((a / c) * t) * -4.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	t_2 = Float64(Float64(Float64(x / Float64(c * z)) * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+80)
		tmp = t_2;
	elseif (t_1 <= -1e-132)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t_1 <= 5e-213)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 5e-22)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	t_2 = ((x / (c * z)) * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -2e+80)
		tmp = t_2;
	elseif (t_1 <= -1e-132)
		tmp = ((t / c) * a) * -4.0;
	elseif (t_1 <= 5e-213)
		tmp = b / (c * z);
	elseif (t_1 <= 5e-22)
		tmp = ((a / c) * t) * -4.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+80], t$95$2, If[LessEqual[t$95$1, -1e-132], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 5e-213], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-22], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e80 or 4.99999999999999954e-22 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot x}{c \cdot z} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right)} \cdot y \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right) \cdot y} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right)} \cdot y \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right)} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{x}{c \cdot z}} \cdot 9\right) \cdot y \]

      9. lower-*.f64 62.8

         \[\leadsto \left(\frac{x}{\color{blue}{c \cdot z}} \cdot 9\right) \cdot y \]

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y} \]

   if -2e80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999999e-133

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 78.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 58.0

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 60.3%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -9.9999999999999999e-133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999977e-213

   1. Initial program 85.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 61.9

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 61.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if 4.99999999999999977e-213 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999954e-22

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 68.5

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 68.5%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 71.3%

      \[\leadsto \left(\frac{a}{c} \cdot t\right) \cdot -4 \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{-132}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-213}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c \cdot z} \cdot 9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(a \cdot -4, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c}\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* a -4.0) t (* (* (/ x z) 9.0) y)) c)))
   (if (<= z -7.4e+26)
     t_1
     (if (<= z 2.8e+112)
       (/ (fma (* 9.0 x) y (fma (* (* -4.0 z) a) t b)) (* c z))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((a * -4.0), t, (((x / z) * 9.0) * y)) / c;
	double tmp;
	if (z <= -7.4e+26) {
		tmp = t_1;
	} else if (z <= 2.8e+112) {
		tmp = fma((9.0 * x), y, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(a * -4.0), t, Float64(Float64(Float64(x / z) * 9.0) * y)) / c)
	tmp = 0.0
	if (z <= -7.4e+26)
		tmp = t_1;
	elseif (z <= 2.8e+112)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a * -4.0), $MachinePrecision] * t + N[(N[(N[(x / z), $MachinePrecision] * 9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -7.4e+26], t$95$1, If[LessEqual[z, 2.8e+112], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.39999999999999977e26 or 2.8000000000000001e112 < z

   1. Initial program 54.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. div-inv N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      4. flip-+ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}} \cdot \frac{1}{z \cdot c} \]

      5. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}}} \cdot \frac{1}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}} \cdot \frac{1}{\color{blue}{z \cdot c}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}} \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

      8. frac-times N/A

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{z}}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b} \cdot c}} \]

      9. div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{z}}}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b} \cdot c} \]

   4. Applied rewrites 56.4%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{1}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)} \cdot c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + -4 \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{a \cdot t}{c} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

      4. associate--l+ N/A

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x \cdot y}{c \cdot z}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      9. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{\frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\color{blue}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\frac{b}{c \cdot z} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}}\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \frac{b}{c \cdot z} + \color{blue}{-4} \cdot \frac{a \cdot t}{c}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \frac{b}{c \cdot z}\right) \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{c \cdot z}\right)}\right) \]

   7. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)} \]

   8. Taylor expanded in c around -inf

      \[\leadsto -1 \cdot \color{blue}{\frac{-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)}{c}} \]
   9. Step-by-step derivation

   10. Applied rewrites 93.9%

       \[\leadsto \frac{\mathsf{fma}\left(-9 \cdot x, \frac{y}{z}, \mathsf{fma}\left(4 \cdot a, t, \frac{-b}{z}\right)\right)}{\color{blue}{-c}} \]

   11. Taylor expanded in b around 0

       \[\leadsto -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{z} + 4 \cdot \left(a \cdot t\right)}{\color{blue}{c}} \]
   12. Step-by-step derivation

   13. Applied rewrites 86.6%

       \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot a, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c} \]

   if -7.39999999999999977e26 < z < 2.8000000000000001e112

   1. Initial program 93.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. associate-+l- N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      4. sub-neg N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{x \cdot 9}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      10. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      11. associate-+l- N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      12. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)} + b\right)}{z \cdot c} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right)\right) + b\right)}{z \cdot c} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right)\right) + b\right)}{z \cdot c} \]

      15. associate-*l* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right)\right) + b\right)}{z \cdot c} \]

      16. distribute-lft-neg-in N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      17. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      18. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      19. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a, t, b\right)}\right)}{z \cdot c} \]

   4. Applied rewrites 91.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot -4, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot -4, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(a \cdot -4, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+104}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* a -4.0) t (* (* (/ x z) 9.0) y)) c)))
   (if (<= z -1.16e-52)
     t_1
     (if (<= z 5e+104) (/ (fma (* y x) 9.0 b) (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((a * -4.0), t, (((x / z) * 9.0) * y)) / c;
	double tmp;
	if (z <= -1.16e-52) {
		tmp = t_1;
	} else if (z <= 5e+104) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(a * -4.0), t, Float64(Float64(Float64(x / z) * 9.0) * y)) / c)
	tmp = 0.0
	if (z <= -1.16e-52)
		tmp = t_1;
	elseif (z <= 5e+104)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a * -4.0), $MachinePrecision] * t + N[(N[(N[(x / z), $MachinePrecision] * 9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.16e-52], t$95$1, If[LessEqual[z, 5e+104], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1599999999999999e-52 or 4.9999999999999997e104 < z

   1. Initial program 60.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. div-inv N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      4. flip-+ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}} \cdot \frac{1}{z \cdot c} \]

      5. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}}} \cdot \frac{1}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}} \cdot \frac{1}{\color{blue}{z \cdot c}} \]

      7. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b}} \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

      8. frac-times N/A

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{z}}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b} \cdot c}} \]

      9. div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{z}}}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) \cdot \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) - b \cdot b} \cdot c} \]

   4. Applied rewrites 61.7%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{1}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)} \cdot c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + -4 \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{a \cdot t}{c} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

      4. associate--l+ N/A

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x \cdot y}{c \cdot z}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      9. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{\frac{y}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\color{blue}{c \cdot z}}, 9, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\frac{b}{c \cdot z} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}}\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \frac{b}{c \cdot z} + \color{blue}{-4} \cdot \frac{a \cdot t}{c}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \frac{b}{c \cdot z}\right) \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{c \cdot z}\right)}\right) \]

   7. Applied rewrites 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \frac{y}{c \cdot z}, 9, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)} \]

   8. Taylor expanded in c around -inf

      \[\leadsto -1 \cdot \color{blue}{\frac{-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)}{c}} \]
   9. Step-by-step derivation

   10. Applied rewrites 94.7%

       \[\leadsto \frac{\mathsf{fma}\left(-9 \cdot x, \frac{y}{z}, \mathsf{fma}\left(4 \cdot a, t, \frac{-b}{z}\right)\right)}{\color{blue}{-c}} \]

   11. Taylor expanded in b around 0

       \[\leadsto -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{z} + 4 \cdot \left(a \cdot t\right)}{\color{blue}{c}} \]
   12. Step-by-step derivation

   13. Applied rewrites 84.3%

       \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot a, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c} \]

   if -1.1599999999999999e-52 < z < 4.9999999999999997e104

   1. Initial program 93.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 80.4

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 80.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot -4, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+104}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot -4, t, \left(\frac{x}{z} \cdot 9\right) \cdot y\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+163}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \left(\left(t \cdot z\right) \cdot a\right) \cdot -4\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -4.1e+163)
   (* (* (/ t c) a) -4.0)
   (if (<= z -1.16e-52)
     (/ (fma (* 9.0 x) y (* (* (* t z) a) -4.0)) (* c z))
     (if (<= z 9.5e+166)
       (/ (fma (* y x) 9.0 b) (* c z))
       (* (/ -4.0 c) (* t a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.1e+163) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= -1.16e-52) {
		tmp = fma((9.0 * x), y, (((t * z) * a) * -4.0)) / (c * z);
	} else if (z <= 9.5e+166) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = (-4.0 / c) * (t * a);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -4.1e+163)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (z <= -1.16e-52)
		tmp = Float64(fma(Float64(9.0 * x), y, Float64(Float64(Float64(t * z) * a) * -4.0)) / Float64(c * z));
	elseif (z <= 9.5e+166)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(-4.0 / c) * Float64(t * a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -4.1e+163], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, -1.16e-52], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+166], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 / c), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.0999999999999999e163

   1. Initial program 29.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 40.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 77.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 77.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 81.5%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -4.0999999999999999e163 < z < -1.1599999999999999e-52

   1. Initial program 84.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. associate-+l- N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      4. sub-neg N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{x \cdot 9}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \mathsf{neg}\left(\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)\right)}{z \cdot c} \]

      10. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      11. associate-+l- N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      12. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)} + b\right)}{z \cdot c} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right)\right) + b\right)}{z \cdot c} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right)\right) + b\right)}{z \cdot c} \]

      15. associate-*l* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right)\right) + b\right)}{z \cdot c} \]

      16. distribute-lft-neg-in N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      17. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      18. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      19. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a, t, b\right)}\right)}{z \cdot c} \]

   4. Applied rewrites 82.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}}{z \cdot c} \]

   5. Taylor expanded in z around inf

      \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}\right)}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(a \cdot \left(t \cdot z\right)\right) \cdot -4}\right)}{z \cdot c} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(a \cdot \left(t \cdot z\right)\right) \cdot -4}\right)}{z \cdot c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)} \cdot -4\right)}{z \cdot c} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)} \cdot -4\right)}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\color{blue}{\left(z \cdot t\right)} \cdot a\right) \cdot -4\right)}{z \cdot c} \]

      6. lower-*.f64 70.9

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\color{blue}{\left(z \cdot t\right)} \cdot a\right) \cdot -4\right)}{z \cdot c} \]

   7. Applied rewrites 70.9%

      \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(z \cdot t\right) \cdot a\right) \cdot -4}\right)}{z \cdot c} \]

   if -1.1599999999999999e-52 < z < 9.49999999999999984e166

   1. Initial program 92.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 78.6

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 78.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   if 9.49999999999999984e166 < z

   1. Initial program 42.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 60.8%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 78.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 78.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 78.8%

      \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{\frac{-4}{c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+163}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \left(\left(t \cdot z\right) \cdot a\right) \cdot -4\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+163}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-171}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(t \cdot z\right) \cdot a\right) \cdot -4\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -4.1e+163)
   (* (* (/ t c) a) -4.0)
   (if (<= z -1.85e-171)
     (/ (fma (* y x) 9.0 (* (* (* t z) a) -4.0)) (* c z))
     (if (<= z 9.5e+166)
       (/ (fma (* y x) 9.0 b) (* c z))
       (* (/ -4.0 c) (* t a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.1e+163) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= -1.85e-171) {
		tmp = fma((y * x), 9.0, (((t * z) * a) * -4.0)) / (c * z);
	} else if (z <= 9.5e+166) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = (-4.0 / c) * (t * a);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -4.1e+163)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (z <= -1.85e-171)
		tmp = Float64(fma(Float64(y * x), 9.0, Float64(Float64(Float64(t * z) * a) * -4.0)) / Float64(c * z));
	elseif (z <= 9.5e+166)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(-4.0 / c) * Float64(t * a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -4.1e+163], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, -1.85e-171], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+166], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 / c), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.0999999999999999e163

   1. Initial program 29.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 40.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 77.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 77.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 81.5%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -4.0999999999999999e163 < z < -1.85000000000000006e-171

   1. Initial program 86.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{b + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b}}{z \cdot c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, a \cdot \left(t \cdot z\right), b\right)}}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, b\right)}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, b\right)}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, b\right)}{z \cdot c} \]

      8. lower-*.f64 59.1

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, b\right)}{z \cdot c} \]

   5. Applied rewrites 59.1%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, b\right)}}{z \cdot c} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\left(x \cdot y\right) \cdot 9 + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(a \cdot \left(t \cdot z\right)\right) \cdot -4}\right)}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(a \cdot \left(t \cdot z\right)\right) \cdot -4}\right)}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)} \cdot -4\right)}{z \cdot c} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)} \cdot -4\right)}{z \cdot c} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \left(\color{blue}{\left(z \cdot t\right)} \cdot a\right) \cdot -4\right)}{z \cdot c} \]

      12. lower-*.f64 69.6

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \left(\color{blue}{\left(z \cdot t\right)} \cdot a\right) \cdot -4\right)}{z \cdot c} \]

   8. Applied rewrites 69.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, \left(\left(z \cdot t\right) \cdot a\right) \cdot -4\right)}}{z \cdot c} \]

   if -1.85000000000000006e-171 < z < 9.49999999999999984e166

   1. Initial program 93.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 81.7

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 81.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   if 9.49999999999999984e166 < z

   1. Initial program 42.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 60.8%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 78.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 78.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 78.8%

      \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{\frac{-4}{c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+163}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-171}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(t \cdot z\right) \cdot a\right) \cdot -4\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+64}:\\ \;\;\;\;\left(\left(\frac{1}{c} \cdot t\right) \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -8.6e+64)
   (* (* (* (/ 1.0 c) t) a) -4.0)
   (if (<= z 9.5e+166)
     (/ (fma (* y x) 9.0 b) (* c z))
     (* (/ -4.0 c) (* t a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8.6e+64) {
		tmp = (((1.0 / c) * t) * a) * -4.0;
	} else if (z <= 9.5e+166) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = (-4.0 / c) * (t * a);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -8.6e+64)
		tmp = Float64(Float64(Float64(Float64(1.0 / c) * t) * a) * -4.0);
	elseif (z <= 9.5e+166)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(-4.0 / c) * Float64(t * a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -8.6e+64], N[(N[(N[(N[(1.0 / c), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 9.5e+166], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 / c), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5999999999999995e64

   1. Initial program 56.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 63.8%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 68.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 68.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 66.3%

      \[\leadsto \left(a \cdot \left(t \cdot \frac{1}{c}\right)\right) \cdot -4 \]

   if -8.5999999999999995e64 < z < 9.49999999999999984e166

   1. Initial program 91.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 76.4

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 76.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   if 9.49999999999999984e166 < z

   1. Initial program 42.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 60.8%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 78.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 78.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 78.8%

      \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{\frac{-4}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+64}:\\ \;\;\;\;\left(\left(\frac{1}{c} \cdot t\right) \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-53}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 10^{+92}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7e-53)
   (* (* (/ t c) a) -4.0)
   (if (<= z 1e+92) (/ b (* c z)) (* (/ -4.0 c) (* t a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7e-53) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= 1e+92) {
		tmp = b / (c * z);
	} else {
		tmp = (-4.0 / c) * (t * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-7d-53)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (z <= 1d+92) then
        tmp = b / (c * z)
    else
        tmp = ((-4.0d0) / c) * (t * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7e-53) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= 1e+92) {
		tmp = b / (c * z);
	} else {
		tmp = (-4.0 / c) * (t * a);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7e-53:
		tmp = ((t / c) * a) * -4.0
	elif z <= 1e+92:
		tmp = b / (c * z)
	else:
		tmp = (-4.0 / c) * (t * a)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7e-53)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (z <= 1e+92)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(-4.0 / c) * Float64(t * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7e-53)
		tmp = ((t / c) * a) * -4.0;
	elseif (z <= 1e+92)
		tmp = b / (c * z);
	else
		tmp = (-4.0 / c) * (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7e-53], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 1e+92], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 / c), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999987e-53

   1. Initial program 66.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 55.4

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 55.4%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 54.0%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -6.99999999999999987e-53 < z < 1e92

   1. Initial program 93.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 49.1

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 49.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if 1e92 < z

   1. Initial program 54.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 71.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 71.4%

      \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{\frac{-4}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-53}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 10^{+92}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{c} \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-53}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 10^{+92}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7e-53)
   (* (* (/ t c) a) -4.0)
   (if (<= z 1e+92) (/ b (* c z)) (* (/ (* t a) c) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7e-53) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= 1e+92) {
		tmp = b / (c * z);
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-7d-53)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (z <= 1d+92) then
        tmp = b / (c * z)
    else
        tmp = ((t * a) / c) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7e-53) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= 1e+92) {
		tmp = b / (c * z);
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7e-53:
		tmp = ((t / c) * a) * -4.0
	elif z <= 1e+92:
		tmp = b / (c * z)
	else:
		tmp = ((t * a) / c) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7e-53)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (z <= 1e+92)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7e-53)
		tmp = ((t / c) * a) * -4.0;
	elseif (z <= 1e+92)
		tmp = b / (c * z);
	else
		tmp = ((t * a) / c) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7e-53], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 1e+92], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999987e-53

   1. Initial program 66.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   4. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z}}{c}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 55.4

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 55.4%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 54.0%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -6.99999999999999987e-53 < z < 1e92

   1. Initial program 93.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 49.1

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 49.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if 1e92 < z

   1. Initial program 54.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 71.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   5. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-53}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 10^{+92}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{c} \cdot -4\\ \mathbf{if}\;z \leq -7 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+92}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ (* t a) c) -4.0)))
   (if (<= z -7e-53) t_1 (if (<= z 1e+92) (/ b (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * a) / c) * -4.0;
	double tmp;
	if (z <= -7e-53) {
		tmp = t_1;
	} else if (z <= 1e+92) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * a) / c) * (-4.0d0)
    if (z <= (-7d-53)) then
        tmp = t_1
    else if (z <= 1d+92) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * a) / c) * -4.0;
	double tmp;
	if (z <= -7e-53) {
		tmp = t_1;
	} else if (z <= 1e+92) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * a) / c) * -4.0
	tmp = 0
	if z <= -7e-53:
		tmp = t_1
	elif z <= 1e+92:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * a) / c) * -4.0)
	tmp = 0.0
	if (z <= -7e-53)
		tmp = t_1;
	elseif (z <= 1e+92)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * a) / c) * -4.0;
	tmp = 0.0;
	if (z <= -7e-53)
		tmp = t_1;
	elseif (z <= 1e+92)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -7e-53], t$95$1, If[LessEqual[z, 1e+92], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999987e-53 or 1e92 < z

   1. Initial program 61.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 62.4

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   5. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]

   if -6.99999999999999987e-53 < z < 1e92

   1. Initial program 93.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 49.1

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 49.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 35.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (c * z)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (c * z)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (c * z);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
4. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   2. lower-*.f64 34.1

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

5. Applied rewrites 34.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 80.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))